Two-tier voting: Measuring inequality and specifying the inverse power problem

There are many situations in which different groups make collective decisions by committee voting, with
each group represented by a single person. This paper is about two closely related problems. The first
is that of how to measure the inequality of a voting system in such a setting. The second is the inverse
power problem: the problem of finding voting systems that approximate equal indirect voting power
as well as possible. I argue that the coefficient of variation is appropriate to measure the inequality of a
voting system and to specify the inverse problem. I then show how specifying the inverse problem with
the coefficient of variation compares to using existing objective functions.